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Philosopher Rebecca Newberger Goldstein (who is Steven Pinker's wife) is interviewed here on "What Plato Can Teach Us." She's asked the question: "Was Plato a “Platonist” in the modern sense of being committed to a claim about the existence of abstract entities, numbers for example?"
Goldstein replies:
"The one area of philosophy in which Platonism is constantly referred to is philosophy of mathematics. There was apparently a survey done by the American Mathematical Association and something like 98 per cent of mathematicians described themselves as “Platonists”. There is [in mathematics] very much a sense that you’re discovering rather than inventing. So this is a kind of commitment to the existence of the abstract, but necessarily in insolation from the physical—the structure of physical reality is given by the abstract, but the abstract can’t be reduced to sensory particulars. So it doesn’t have to involve a commitment to a kind of Platonic “heaven” that Russell, for example, makes fun of; it can be the claim that reality can’t be intelligible without referring to abstractions which cannot themselves be reduced to anything other than themselves."
The discussion of abstract objects interests me because it runs against physicalism, and theism is non-physicalism.
See the current discussions William Lane Craig is involved in re. abstract objects and theism (e.g., Beyond the Control of God: Six Views on the Problem of God and Abstract Objects, edited by Paul Gould).
